In Exercises 62-65, determine whether each statement "makes...

In Exercises $62-65$, determine whether each statement "makes sense" or "does not make sense" and explain your reasoning.
When I use graphing to solve an inconsistent system, the lines should look parallel, and I can always use slope to confirm that they really are.

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Key Concepts

Parallel Lines

Parallel lines are lines in a plane that never intersect, regardless of how far they are extended. In the context of graphing linear systems, if the lines represented by the equations are parallel, it confirms that the system is inconsistent, as there is no common solution or point of intersection.

Graphing Linear Equations

Graphing linear equations involves representing each equation as a line on a coordinate plane to visually determine the points of intersection. This method aids in identifying whether a system has a unique solution, infinitely many solutions, or no solution at all.

Inconsistent Systems

An inconsistent system is one in which there are no solutions because the equations represent lines that do not intersect. This occurs in linear systems when the lines have the same slope but different y-intercepts, meaning they are parallel and never meet.

Slope

The slope of a line is a measure of its steepness and direction, defined by the ratio of the vertical change to the horizontal change between any two points on the line. In the context of linear systems, comparing slopes is essential because lines with the same slope are parallel, which directly relates to the concept of an inconsistent system.

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